They are not. Set is an interface that extends from Collection interface and its just a sub-interface... Its not an interface within another interface. From the specs here I see that Sun calls an interface within another interface as a "nested interface" I guess this nesting of an interface in another has only to do with some namespace resolution...

Vishwanath brings up an important point. There is a rather complicated difference between a "nested class" and an "inner class"... I'm not going to try to explain it because I don't remember it correctly, but you might want to review that. Then it's quite likely that "inner interface" and "nested interface" would be the same concepts.